Detailed derivations and further analysis are presented of a recent concept for a plasma-based accelerator scheme incorporating a strong circularly polarised magnetic wiggler field producing relativistic-strength diamagnetic transverse plasma currents. The increase in the plasma Lorentz factor leads to a substantial increase in the longitudinal component of the wave electric field and therefore of the acceleration rate. It is also found that ultra-high acceleration gradients are possible with relatively low plasma densities and long wave lengths. It also appears possible that the transverse wiggling motion of the electrons of the beam is able to delay the dephasing with the accelerating wave leading to much higher values of the energy gained by the beam at saturation and even electron bunches that have been injected with the "wrong" phase seem to be able to reverse their motion and accelerate to very high energies in short distances.